Check correctness of the equation \(F.S=\frac{1}{2}mv^{2}-\frac{1}{2}mu^{2}\), where F is the force acting on the body, m is the mass of the body, S is the distance travelled when velocity changes from u to v.
Ans: Correct
Check the correctness of relation \(v=\left[\frac{E}{\rho}\right]^{\frac{1}{2}}\). Where; \(v = \) velocity of the sound wave, \(E = \) Co-efficient of Elasticity and \(\rho = \) Density of Medium.
Ans: Correct
Check the correctness of the relation \(V=\frac{\pi p r^{4}}{8\eta l}\). Where; \( V \) is Rate of flow of liquid through a tube, \(\eta\) is Viscosity of the liquid, \( r \) is the Radius of the tube having length \(l\) and \(p\) is the pressure difference between the ends of tube.
Ans: Correct
Check the dimensional correctness of the equation of escape velocity \(v=\sqrt{\frac{2GM}{R}}\). Where; G is the Gravitational Constant, M is Mass of the satellite and R is the Radius of circular orbit.
Ans: Correct
Check the accuracy of the relation, \(S=\frac{mgl^{3}}{4bd^{3}Y}\). Where: S is the depression produced in the middle of a bar of length l, breadth b and depth d, when it is loaded in the middle with mass m, Y is the Young’s modulus of the material of the bar.
Ans: Correct
Check the correctness of the relation \(\tau=I\alpha\). Where; \(\tau\) is torque acting on the object, \(I\) is moment of inertia and \(\alpha\) is angular acceleration.
Ans: Correct
Consider an equation; \(\frac{1}{2}mv^{2}=mgh\). Where; m is mass of the object, v is velocity of the object, g is acceleration due to gravity and h is height. Check weather the equation is dimensionally correct.
Ans: Correct
The viscous force \(F=6\pi r \eta v\). Where; \(\eta\) is coefficient of viscosity of liquid through which object is falling, \(r\) is radius of the object falling through given viscous medium, \(v\) is a constant velocity (also, known as terminal velocity) with which object falling through the viscous medium. Check the dimensional correctness of the equation.
Ans: Correct
Check the dimensional correctness of the following equation; \(h=\frac{2S Cos\theta}{r \rho g}\). Where; \(h\) is capillary rise of liquid through narrow tube, \(S\) is surface tension of given liquid, \(\rho\) is density of the liquid and \(g\) is acceleration due to gravity.
Ans: Correct
Check by the method of dimensional analysis wheather the following equation is correct or not, dimensionally. \(T=2\pi\sqrt\frac{l}{g}\). Where; \(T\) is time period of pendulum, \(l\) is effective length of the pendulum, \(g\) is acceleration due to gravity.
Ans: Correct
Time period of oscillation of a drop of radius \(r\), density \(\rho\) and surface tension is \(S\) is given by; \(T=k\sqrt\frac{\rho r^{3}}{S}\). Check the correctness of the given equation.
Ans: Correct
A physical quantity is given by; \(T=2\pi \sqrt\frac{ml^{3}}{3Yq}\). Check the correctness of the equation. Where; \(T\) is time period of bar having length l. \(m\) is the mass of the object. \(Y\) is young’s modulus. Also, What is the dimension of quantity \(q\) .
